Short-sales Price Efficiency

To investigate directly how short-sales affect price efficiency, we calculate various measures of price efficiency for the pilot sample and the non-pilot stocks individually. We therefore conduct a variance-ratio test following using a set of sampling frequencies to subdivide our year of data.

The number that the resulting ratio deviates from unity can be interpreted as the return auto-correlation. Table 7 shows that the random walk hypothesis cannot be rejected for neither of pilot nor non-pilot stocks. We do find, however, that pilot stocks tend to have a negative auto-correlation, which is reflected in the mean-reverting price behavior that short-sellers exploit. As points out, asset prices where prices are quoted with bid and ask spreads should, if they are efficient, experience negative serial auto-correlation. This market set-up also applies to stocks, it follows from this that one should expect efficiently prices stocks to have some negative serial auto-correlation. As we find negative auto-correlation only for pilot stocks, one could interpret

this as some evidence for pilot stocks being more efficiently priced than non-pilot stocks that do not exhibit negative auto-correlation on average.

Therefore, while we fail to find strong direct evidence for stock prices to be more efficient when short-selling restrictions are revoked; our results provide some tentative evidence that pilot stocks may be priced more efficiently than non-pilot stocks. We do find strong evidence, however, that short-sellers provide liquidity to the market, which in itself is a positive contribution by sellers and therefore implies that, overall, stock-markets benefit from short-selling.

6 Conclusion

This paper looks at short-sales, investigates the information content and trade motivation behind informed short-sales and compares these with regular buys and sales. Short-sales appear to be an important source of liquidity during times of uninformed buying pressure. This appears to make short-sales unprofitable intra-day as prices, pushed up by uninformed trading pressure, temporarily move against short-sellers’ positions. The reversal of prices provides short-sellers with a reasonable return for their liquidity service. To implement this strategy of informed liquidity provision, informed short-sellers seem to rely on both, their understanding of the market environment and private information about fundamental values.

Short-sellers exploit negative earnings surprises, which they typically do not seem to anticipate, however. Rather, short-sellers appear to react to the public announcement of negative surprises, suggesting that the typical short-seller does not have insider information but rather appears to be a -type skilled information analyst. Short-selling constraints seem to affect the price efficiency, though it appears that prices – even with short-selling restrictions – are fairly efficiently priced. Further, investors are more likely to be exposed to informed short-sales when

trading on the NYSE while short-sales on alternative trading venues are more likely to be used for inventory management and hedging purposes.

Public investors may find the results interesting that trading on exchanges other than the NYSE, the avoidance of short-term momentum strategies, and the reduction of trading activity during periods of low liquidity may protect them from adverse selection losses associated with exposure to informed short-sellers. Informed short-sellers seem not to use corporate insider information but rather appear to provide liquidity, which may be an interesting finding for regulators. Thus, short-sales are a net positive contribution to the financial markets, as they improve price efficiency and provide liquidity that keeps prices from diverging too much from fundamentals.

Among the limitations of this study is the short time horizon, although the large number of daily and intra-daily observations that are used imply sufficient statistical validity of the empirical results. It would be interesting to investigate further in future research one of the main issues looked at in this paper, i.e., the contribution of short-selling restrictions to price efficiency and financial market stability. In particular, looking at short-selling trading patters in pilot and non-pilot stocks during market downturns could improve the understanding about the benefits and costs of short-selling restrictions.

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Figure 1 – Distribution of Information Content of Short-sales

This figure shows the empirical distribution of the information content of short-sales normalized for each firm individually over various horizons. Panel A shows the distribution of short sales and Panel B shows the distribution of regular sales and buys

Panel A –Distribution of Information Content of Short-sales

Short Sales - Information Contents over 60 Minutes

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Short Sales - Information Contents over 1 day

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Short Sales - Information Contents over 5 days

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Short Sales -Information Contents over 10 days

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Panel B –Distribution of Information Content of Regular Sales and Buys

Regular Sales and Buys - Information Contents over 60 Minutes

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Regular Sales and Buys - Information Contents over 1 day

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Regular Buys and Sales - Information Contents over 5 days

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

Regular Buys and Sales -Information Contents over 10 days

0.0

-4.05 -3.68 -3.30 -2.93 -2.55 -2.18 -1.80 -1.43 -1.05 -0.68 -0.30 0.08 0.45 0.83 1.20 1.58 1.95 2.33 2.70 3.08 3.45 3.83

Standardized IA

Frequency (%)

35

Table 1 – Summary Statistics Explanatory Variables

This table lists the names of the variables used in this paper in column Variable Name and the definition used to construct the respective variable in the column Definition.

Variable Definition Abnormal returns The residual from a regression of daily stock returns in excess of the risk-free rate on daily market excess returns

and the SMB and HML factor returns during the time-period covered by this study.

Announcement surprise The cumulative post-announcement returns during the five days that follow the announcement including the announcement day.

AvVolume The yearly average of total daily dollar trading volume of a particular stock.

Beta The stock-level beta calculated using the Fama and French (1992) methodology.

Bid-ask spread The daily time-weighted average of the intra-day difference between the BBO quotes scaled by the quote-mid point.

BTM The sum of common equity, investment tax credits, and deferred taxes less the total value of preferred shares divided by firm size.

Dollar imbalance The residual from a stock-level regression of dollar imbalance on Turnover.

Dollar volume The daily sum of the $ trade volume in the stocks of a particular firm.

Firm size The daily market capitalization measured as the product of total shares outstanding and the closing stock price.

FutureReturn The return in a particular stock over the next month and is calculated as the first difference of the logarithm of the stock price today and the logarithm of the last valid stock price observation exactly one month later than today.

IA The daily trade size-weighted average of the difference between the quote mid-point right before a transaction and the quote mid-point some minutes or trading days later scaled by the first quote mid-point.

IAi,d The Trade size-weighted mean (or the Sum) of IA of all short-sales (or buys or regular sales) during one-minute intra-day interval d. IA is multiplied by the trade size and thus expressed in dollars if Dollar Volume is used on the right hand side of the regression in Panels B and C in Table 4.

Inventory The level of inventory of liquidity providers a particular stock. This is approximated by the net daily number of shares bought and sold multiplied by minus the closing stock price and is normalized for each stock individually to a mean of zero and a variance of one.

InventoryDummyj A dummy variable that is equal to one if the level of inventory in a particular stock is in inventory-size group j and zero otherwise. Inventory size Groups 1 to 5 are defined as the five inventory quintiles evaluated on the individual stock-level with Group 1 being the lowest inventory.

Market-adjusted returns The residual from a regression of daily stock returns in excess of the risk-free rate on daily market excess returns.

Market-adjusted short volume The standardized stock-level short-selling volume less the market value-weighted average standardized relative short-selling volume of that day.

MIA The market value-weighted average IA.

Momentum returns The compounded daily returns over the past five days.

MVolumed The market value-weighted average of the Trade size-weighted mean (or Sum) of the volume sold short, bought, or regularly sold during one-minute intra-day interval d.

Post-announcement returns Captured alternatively by Raw Returns or Abnormal Returns, which are calculated as the residual from a regression of stock returns in excess of the risk-free rate on market excess returns and the SMB and HML factor returns.

Raw returns Daily stock returns.

Relative Volume The ratio of short Dollar Volume to total daily dollar trading volume.

Returns (cumul.) around announcements

The cumulative return during the five days that follow quarterly earnings announcements.

Share order-imbalance The net number of shares bought and sold during a particular day.

ShortVolume The dollar volume sold short scaled by the total trading volume on that day.

Tick size The inverse of the daily stock price.

Trade-type This variable specifies the short-sale data set considered, which comprises either All trades, only NYSE trades, only short-sales routed Off-NYSE, only short-sales that are Exempt from short-selling restrictions, only short-sales that are Non-exempt from short-selling restrictions, short-sales of stocks that are part of the Reg SHO Pilot sample, and short-sales of stocks that are not part of the pilot sample (referred to as Non-pilot).

TradeTypeDummyk A dummy variable that is one if the short-volume data of a particular stock refer to trade-type k and zero otherwise.

Turnover Defined as Dollar volume scaled by the daily market capitalization of a firm.

Volume The US-Dollar value traded during a day.

Volumei,d The trade size-weighted mean of the volume sold short, bought or sold (measured alternatively by Dollar Volume, Relative Volume, or Turnover) in stock i during one-minute intra-day interval d.

Table 2 – Sample Summary Statistics

This table shows summary statistics of the data used in this study. Panel A reports the number of Observations, the Mean and Median values and the first and third quartile (Q1 and Q3) of the IA, dollar volume, and turnover data used in this study. The statistics are based on firm-level means. The columns Data Type and Variable indicate the broad area the respective variable refers to and the variable name, respectively. Appended to the variable names in parentheses are the units of measurement, whereby 10,000 $ and bp denote ten thousand dollars and basis points, respectively. Skew and Kurt is the mean of the firm-level skewness and kurtosis values. IA measures the information content of Short-sales or of Other Trades, defined as the value-weighted average of long buys and sales not classified as shorts by firms that also have short sales data on the particular date.

The columns % positive, % > 1 σ, and % > 2 σ denote the mean percentage of firm-level IA observations that are positive, more than 1 standard deviation and more than 2 standard deviations above the firm-level mean-IA, respectively. The column Annualized shows the IA values calculated over at least one day annualized to make the measure better comparable across horizons assuming a 250 day-count. The column P-val shows the p-value of a non-parametric two-sided Kruskal-Wallis test of equality in medians between the short-sales IA and the IA of regular buys and sales estimated over the same horizon. Panel B shows the Mean and Median difference (in basis points) between IA of short sales and the IA of regular buys and sales (which are grouped together) by Quintiles (with 1 being the smallest and 5 the largest group) based on Firm size, Beta, Book-to-Market, the Bid-ask spread, Tick-size, Volume, and the Number of trades. Volume and the Number of trades are calculated over the sum of short-sales, and regular buys and sales. Panel C shows the number of observations (Obs.), the Mean and Median values and the first and third quartile (Q1 and Q3) of the explanatory variables used in this study. The columns Data Type and Variable indicate the broad area the respective variable refers to and the variable name, respectively. Appended to the variable

The columns % positive, % > 1 σ, and % > 2 σ denote the mean percentage of firm-level IA observations that are positive, more than 1 standard deviation and more than 2 standard deviations above the firm-level mean-IA, respectively. The column Annualized shows the IA values calculated over at least one day annualized to make the measure better comparable across horizons assuming a 250 day-count. The column P-val shows the p-value of a non-parametric two-sided Kruskal-Wallis test of equality in medians between the short-sales IA and the IA of regular buys and sales estimated over the same horizon. Panel B shows the Mean and Median difference (in basis points) between IA of short sales and the IA of regular buys and sales (which are grouped together) by Quintiles (with 1 being the smallest and 5 the largest group) based on Firm size, Beta, Book-to-Market, the Bid-ask spread, Tick-size, Volume, and the Number of trades. Volume and the Number of trades are calculated over the sum of short-sales, and regular buys and sales. Panel C shows the number of observations (Obs.), the Mean and Median values and the first and third quartile (Q1 and Q3) of the explanatory variables used in this study. The columns Data Type and Variable indicate the broad area the respective variable refers to and the variable name, respectively. Appended to the variable

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